Exam 13: Rotation II: a Conservation Approach

The object shown below has mass m and velocity . The direction of its angular momentum vector with respect to an axis perpendicular to the page through point O is

A uniform solid sphere rolls without slipping along a horizontal surface. What fraction of its total kinetic energy is in the form of rotational kinetic energy about the CM?

A particle whose mass is 2 kg moves in the xy plane with a constant speed of 3 m/s in the x direction along the line y = 5. What is its angular momentum (in kg⋅m²/s) relative to the origin?

Five objects of mass m move at velocity at a distance r from an axis of rotation perpendicular to the page through point A, as shown below. The one that has zero angular momentum about that axis is

If M = 0.50 kg, L = 1.2 m, and the mass of each connecting rod shown is negligible, what is the rotational inertia about an axis perpendicular to the paper through the center of mass? Treat the mass as particles. ​ ​

Four identical particles (mass of each = 0.40 kg) are placed at the vertices of a rectangle (2.5 m × 4.0 m) and held in those positions by four light rods which form the sides of the rectangle. What is the rotational inertia of this rigid body about an axis that passes through the mid-points of the shorter sides and is parallel to the longer sides?

A solid cylinder of radius R = 1.0 m and mass 10 kg rotates about its axis. When its angular velocity is 10 rad/s, its angular momentum (in kg⋅m²/s) is

Stars originate as large bodies of slowly rotating gas. Because of gravity, these clumps of gas slowly decrease in size. The angular velocity of a star increases as it shrinks because of

A 0.5 kg fish, hooked as shown below, starts to swim away at a speed of 3 m/s. The angular momentum of the fish relative to the hand holding the fishing rod is about

Three particles, each of which has a mass of 80 g, are positioned at the vertices of an equilateral triangle with sides of length 60 cm. The particles are connected by rods of negligible mass. What is the moment of inertia of this rigid body about an axis that is parallel to one side of the triangle and passes through the respective midpoints of the other two sides?

In the figure, a 1.6-kg weight swings in a vertical circle at the end of a string having negligible weight. The string is 2 m long. If the weight is released with zero initial velocity from a horizontal position, its angular momentum (in kg⋅m²/s) at the lowest point of its path relative to the center of the circle is approximately

If L represents angular momentum, I represents rotational inertia, p represents linear momentum, m represents mass, and r represents a distance, which of the following can represent kinetic energy?

A car of mass 1000 kg moves with a speed of 50 m/s on a circular track of radius 100 m. What is the magnitude of its angular momentum (in kg⋅m²/s) relative to the center of the race track?

A space station out beyond the solar system is rotating with constant angular velocity. A spaceship heading into the station along a diameter of the station, uses its rockets to brake, and then docks inside the station at its center. When the spaceship docks, the angular momentum of the system consisting of the station and ship

A wheel (radius = 12 cm) is mounted on a frictionless, horizontal axle that is perpendicular to the wheel and passes through the center of mass of the wheel. A light cord wrapped around the wheel supports a 0.40-kg object. If released from rest with the string taut, the object is observed to fall with a downward acceleration of 3.0 m/s². What is the rotational inertia (of the wheel) about the given axle?

Two particles (m1 = 0.20 kg, m² = 0.30 kg) are positioned at the ends of a 2.0-m long rod of negligible mass. What is the rotational inertia of this rigid body about an axis perpendicular to the rod and through the center of mass?

A particle whose mass is 2 kg moves in the xy plane with a constant speed of 3 m/s along the direction . What is its angular momentum (in kg⋅m²/s) relative to the origin?

A hockey puck traveling at speed v on essentially frictionless ice collides elastically with one end of a straight stick lying flat on the ice. In this collision

A mass m = 4.0 kg is connected, as shown, by a light cord to a mass M = 6.0 kg, which slides on a smooth horizontal surface. The pulley rotates about a frictionless axle and has a radius R = 0.12 m and a rotatinal inertia I = 0.090 kg⋅m². The cord does not slip on the pulley. What is the magnitude of the acceleration of m? ​ ​

What is the angular momentum of the Moon about the Earth? The mass of the Moon is 7.35 × 10²² kg, the center-to-center separation of the Earth and the Moon is 3.84 × 10⁵ km, and the orbital period of the Moon is 27.3 days. Ignore the small offset of the center of mass of the system from the center of the Earth in your calculation.